There is just one place in the 1570 Low Mass where the words explicitly invite the congregation to respond, that is the Orate, fratres ... . However while the words are of course retained, the rubrics up to 1960 require the priest, after the opening words said aloud and towards the congregation, to turn away and complete the request silently.
What then of the Solemn Mass? We have the claim in Quo primum that the group commissioned to prepare the Missal worked diligently and arduously to discern the "original rite and form of the Holy Fathers". But we do not even know the composition of the group, let alone what they reported. It is known that even within Rome the major basilicas and the tituli each had their own customs, and that many dioceses and nations had their own uses which differed in details, particularly in ways of engaging the people. For example Sarum Use, which had been spread throughout England by Royal Decree, had processions, stational altars, and use of the pax-brede.
Faced with this multiplicity the 1570 adopted the simplest of solutions. The priest would continue to say a Low Mass, adding the interactions for blessing incense, singing the incipit of the Gloria and Credo etc. And all the other parts which in the Curia would be filled by functionaries employed for the purpose, and probably in minor orders, would continue undisturbed. All the multifarious forms used elsewhere to address pastoral concerns would be ignored fall into desuetude or be suppressed. That meant setting aside both what the Council of Trent had desired (or commanded) and the whole of Aquinas' explanations of the didactic functions of liturgy.
Thomas Aquinas Distinction 8 of Book IV of his Commentary on the Sentences of Peter Lombard. can be found in English translation here: https://www.newliturgicalmovement.org/2015/07/st-thomas-aquinass-early-commentary-on.html#disqus_thread
The commands of the Council of Trent for teaching the people during Mass are found in Session XXII ch viii https://www.capdox.capuchin.org.au/reform-resources-16th-century/sources/the-canons-and-decrees-of-the-council-of-trent/#post-2439-_Toc529040197 and the corresponding discussion by Aquinas is at https://www.newadvent.org/summa/4083.htm#article4